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Robust topology optimization accounting for misplacement of material

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Abstract

The use of topology optimization for structural design often leads to slender structures. Slender structures are sensitive to geometric imperfections such as the misplacement or misalignment of material. The present paper therefore proposes a robust approach to topology optimization taking into account this type of geometric imperfections. A density filter based approach is followed, and translations of material are obtained by adding a small perturbation to the center of the filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued random field. The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined as a weighted sum of the mean value and the standard deviation of the performance of the structure under uncertainty. A sampling method is used to estimate these statistics during the optimization process. The proposed method is successfully applied to three example problems: the minimum compliance design of a slender column-like structure and a cantilever beam and a compliant mechanism design. An extensive Monte Carlo simulation is used to show that the obtained topologies are more robust with respect to geometric imperfections.

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Acknowledgements

The research presented in this paper has been performed within the framework of the KU Leuven - BOF PFV/10/002 OPTEC - Optimization in Engineering Center and the NextTop project sponsored by the Villum Foundation. We also acknowledge support via KUL GOA/10/09 MaNet, FWO G.0320.08 (convex MPC), G.0558.08 (Robust MHE), G.0377.09 (Mechatronics MPC), IWT SBO LeCoPro, IUAP P6/04 DYSCO, FP7-EMBOCON (ICT-248940), FP7-SADCO (MC ITN-264735), ERC HIGHWIND (259 166).

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Authors and Affiliations

  1. Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, 3001, Leuven, Belgium

    Miche Jansen & Geert Lombaert

  2. Department of Electrical Engineering, KU Leuven, Kasteelpark Arenberg 10, 3001, Leuven, Belgium

    Moritz Diehl

  3. Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Nils Koppel’s Allé, Building 404, 2800, Lyngby, Denmark

    Boyan S. Lazarov & Ole Sigmund

  4. Department of Architecture, Urbanism and Planning, KU Leuven, Kasteelpark Arenberg 1, 3001, Leuven, Belgium

    Mattias Schevenels

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  1. Miche Jansen
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  2. Geert Lombaert
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  3. Moritz Diehl
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  4. Boyan S. Lazarov
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  5. Ole Sigmund
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  6. Mattias Schevenels
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Correspondence to Miche Jansen.

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Jansen, M., Lombaert, G., Diehl, M. et al. Robust topology optimization accounting for misplacement of material. Struct Multidisc Optim 47, 317–333 (2013). https://doi.org/10.1007/s00158-012-0835-z

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  • DOI: https://doi.org/10.1007/s00158-012-0835-z

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